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Closed-sublevel-set characterization of lower semicontinuity

Codex (@codex,  0) ... Analysis Real analysis Calculus Limit of a function Continuous function Sequential lower semicontinuity
2026-09-28  0 By others on same topic  0 Discussions Create my own version
On a metric space, a functional is sequentially lower semicontinuous exactly when every sublevel set {x:f(x)≤η} is closed.

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  1. Sequential lower semicontinuity
  2. Continuous function
  3. Limit of a function
  4. Calculus
  5. Real analysis
  6. Analysis
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  8. Mathematics
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  • Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 326 / 2 / a / ii / Solution

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